This is an interesting issue beyond the law. To what extent does owning a phrase or word, even a word you made up, give one rights to how it is used?
On one hand, it would appear that the search engine and those who buy the brand name would be trading on the reputation and work of the owner of the name. It's a basic trademark violation, they say.
On the other hand, attempting to limit how what the user of a search engine sees when they search on the brand would be restricting speech and free trade.
The search engines have point to the fact that it is an auction system which determine who get the exposure from purchasing the keyword, saying that this means that to prohibit use of brand names would be restraining trade.
The issue should decided on what best serves the public good, which is why LVMH points to fakes being sold on the search ads.
The reply on this is that selling fakes is fraud and outside the issue at hand.
I've looked at this for a long time and come to conclusion is that restricting the use of brand names is not appropriate. Of course, there are bad actors that make one reconsider this at times. But, using brand names can be ethical and it should be legal.